In mathematics a binary relation between two sets \(A\) and \(B\) is a collection of ordered pairs \((a,b)\) belonging to the cartesian product \(A\,\times \,B\). In this chapter we present some of the general properties of relations and their operations, as well some special types of relations defined over the same set. A good command of these basic notions is essential for understanding the relational database theory, where a relation is a set of tuples \((a_1, a_2, ..., a_n)\) and each element \(a_j\) is a member of \(A_n\) a data domain (sometimes called an attribute). In the context of databases we also present the notion of key.